Transmit and receive antenna arrays can be used to form multiple-input and multiple-output (MIMO) systems. In a MIMO system, there are two or more antennas at a transmitter and two or more antennas at a receiver. A signal transmitted by a MIMO transmitter may be expressed as a function of data that is to be transmitted and channel state information (CSI). The CSI is a mathematical representation of a signal channel, namely the way in which a signal traverses a communication medium from a sender to a receiver. Therefore, in a MIMO system the CSI represents how each transmitted signal traverses a communication medium from each antenna at the transmitter to each of the antennas at one or more receivers. The CSI of a MIMO system can be exploited at the transmitter in many different ways to improve the performance of a MIMO system. For example, the performance may be improved in the form of increased reliability and capacity of data transmission, especially in comparison with single-input systems.
In many situations, however, the transmitter can only obtain CSI through feedback from the receiver, which usually requires large overhead. The large overhead is caused by processing power being used at the receiver to estimate the CSI and bandwidth being used by the receiver to communicate the CSI back to the transmitter. Further, due to various problems such as channel estimation error and delay in the feedback, the CSI available at the transmitter is imperfect. The imperfect CSI may lead to reduced performance gains of a MIMO system. As such, it is desirable to utilize a MIMO system to improve performance without using CSI. In particular, it is desirable to determine an optimal power allocation of the transmitted signals without CSI based on the signal-to-noise ratio of the layered space-time MIMO system, because such power allocation facilitates decision feedback detection and successive interference cancellation.